Limits and Continuity

Given the function $f(x)$ whose graph includes an inflection point at $(3, 7)$, if $g(x) = f'(x - 2) + 5$, at which $x$-value would the graph of $g$ exhibit a potential local extremum?

When estimating a limit value from a graph, if the y-values from the left and right sides approach different values, but the difference between these values gets smaller and smaller, what can be concluded about the limit?

Based on a graph showing that as x nears negative infinity for function j, j's outputs seem to stabilize around negative seven, how do you denote this observed behavior using limits?

For a function $f$, as $x$ approaches a certain value from both sides, the $y$-values diverge and do not approach the same value. What can be concluded about the limit of $f$ as $x$ approaches that value?

When estimating a limit value from a graph, if the y-values from the left and right sides approach positive infinity, what can be concluded about the limit?

On a graph, the function $f(x)$ approaches positive infinity as $x$ approaches a certain value. What can be concluded about the limit of $f$ as $x$ approaches that value?

What is $\lim_{x \to +\infty} f(x)$ if the graph has a horizontal asymptote at y=7?

When estimating a limit value from a graph, if the y-values from the left and right sides approach different values and the difference between these values increases without bound, what can be concluded about the limit?

When estimating a limit value from a graph, if the y-values from the left and right sides approach different infinities (positive and negative), what can be concluded about the limit?

If the graph of a function $f$ approaches a value of 3 as $x$ approaches 2 from the left side, what is the limit of $f(x)$ as $x$ approaches 2 from the left?